This invention relates to apparatus for calculating the amplitude value of a sinusoidal wave, more particularly sinusoidal current or voltage of an electric power system.
To adequately operate a certain type of a protective relay for an electric power system it is necessary to calculate the amplitude value of the AC voltage or current of the power system. For this purpose, it has been the practice to sample at a predetermined interval the sinusoidal voltage, or current or both of the power system, convert the sample values into digital signals, encode the digital signals and then transmit the encoded digital signals to a receiving end for calculating the amplitude value of the sinusoidal voltage or current. The following two methods have been used to perform such calculation.
A. addition Method. PA0 B. square Method
According to this method the absolute values of a plurality of data samples in one-half cycle of the input alternating current are added together, and the sum is multiplied with a predetermined coefficient. In an example shown in FIG. 1, an alternating current having a frequency of 50 Hz is sampled at a sampling frequency of 600 Hz, the data samples in one-half cycle are i.sub.m-5 through i.sub.m and the amplitude value I is calculated by the following equation ##EQU1## WHERE I REPRESENTS AN INSTANTANEOUS VALUE, M A TIME SERIES.
The error of calculation according to equation (1) caused by the sampling phase is less than .+-.1.7 %.
From a formula of trigonometric function the following equation (2) holds ##EQU2## This equation shows that the sum of the squares of two data having phase angles different by 90.degree. electrical is equal to the square of the amplitude value of an input alternating current quantity. In the case shown in FIG. 1 wherein an input having a frequency of 50 Hz is sampled at a frequency of 600 Hz, the square of the amplitude value is determined by the following equation. EQU I.sup.2 = i.sub.m.sup.2 + i.sub.m-3.sup.2 (3)
With this equation no error is caused by the sampling phase.
The addition method and the square method described above have the following advantages and disadvantages. Thus, according to the square method the amplitude value is determined by two data dephased by 90.degree. electrical, whereas according to the addition method it is necessary to use a plurality of data samples which are sampled from one half cycle of the input alternating current, thus in the example shown in FIG. 1 six data samples. This means that the operation device requires a larger member of memory elements, and that it is necessary to use a higher sampling frequency to attain the desired object.
Although the addition method is advantageous in that a quantity proportional to the amplitude value can readily be obtained by a simple addition operation, the square method requires a mathematical operation to obtain a square root according to equation (3). Where the protection of a power system is performed by an electronic computer in response to digital signals, the operation for determining the square root requires much longer time than the addition operation.